IR Collar

Constructing an IR collar you buy an IR call option and sell an IR put option. Why not buy both? Wouldn’t you be protected from both upsides and downsides?

That would cost something. The argument here is to sell a put and use the proceeds to buy a call.

the collar is meant to hedge a floating rate liability, by selling the put you fund the call option premium (so zero or near zero cost) and create a band with which you ensure your liabiliaty cost

You can also protect against falling interest rates (if you have a floating rate asset) by buying a floor and selling a cap.

you could buy both, but then you have to absorb costs. If you buy one and sell the other, there is no cost